Course Syllabus

• First order equations.
• First order linear and nonlinear equations: analytic methods for solving linear equations, separable equations and exact equations.
• Modeling with linear first order equations: exponential growth and decay; mixing problems; interest rates; and others.
• Modeling with nonlinear first order equations, geometric methods and qualitative analysis, population models, phase portrait and classification of equilibrium points.
• Second order equations.
• Theory, linearity principle.
• Homogenous second order linear differential equations with constant coefficients. Real, complex roots, and repeated roots.
• Inhomogeneous second order linear differential equations: methods of undetermined coefficients.
• Modeling with linear second order equations: Mechanical and electrical oscillations. Forcing and resonances.
• Laplace transform methods.
• Laplace transform for initial value problems.
• Discontinuous forcing.
• Impulse functions and convolutions.
• Systems of linear differential equations: eigenvalues and eigenvectors, phase portraits.
• Review of linear algebra: matrices, eigenvalues and eigenvectors.
• System of linear equations with constant coefficients: solving initial value problems with real and complex eigenvalues.
• Classification of equilibrium points, sinks, sources, saddles, centers, spiral sinks and spiral sources.

Prerequisites: Math 131 & 132.

Text: Elementary Differential Equations, 11th edition, by Boyce, DiPrima and Meade.